Variable attenuation network



May 9, 1944 1 P. H. RICHARDSON 2,348,572

`VARIABLE ATTENUATION NETWORK Filed Feb. 20, V1945 2 Sheets-Sheet 1 R2' R ffn 7%6' gw'pz, R2

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ATTORNEK .leieisyer 1944 i VARIABLE ATTENUATIGN NETWORK raul n. Richardson, Chatham, N. J., assigner to Bell Telephone Laboratories, Incorporated, New f York, N. Y., a corporation of New York g Application February 20, 1943, Serial No. 476,512

13 Claims.

This invention relates to attenuation equalizing networks and more particularly to variable equalizers having a plurality of controls for the compensation of transmission lines subject to variation in attenuation.

An object of the invention is to maintain close attenuation regulation .for a transmission line, the attenuation of which changes.

Another object is to provide, over a finite frequency range.a variable attenuation characteristic which may be made to simulate any given curve as closely as desired.

A feature of the invention is a variable attenuation network having a number of controls each of which independently controls an insertion loss characteristic corresponding to one term of a Fourier series.

It is known that any curve, over a limited range, may be analyzed on the basis of a Fourier series, and that if a suiiicient number of terms are employed the curve may be simulated toany desired degree of closeness. In accordance with the present invention there is provided a variable attenuation network comprising a number of associated but independently controlled units each of which furnishes an insertion loss characteristie corresponding to one term of a Fourier series. If enough such units are :provided it is obvious that any attenuation characteristic may be simulated as closely as desired over a nite frequency range. In practice it will usually be found that only a few units will give the required simulation.

Each oi' the units is made up of one or more tandem connected variable attenuation equalizer sections of the type disclosed in United States Patent 2,096,027, issued October 19, 1937, to H. W. Bode. Eachpf these sections comprises a pair of terminal impedances between which is interposedv a variable impedance constituted by a fixed resistor in combination with a subsidiary four-terminal network terminated by a variable resistor. The xed resistor may be connected either In series or in parallel with the associated terminal impedances. Each subsidiary network has an image impedance which is a constant resistance and an image transfer constant the attenuation constant of which is lindependent of frequency and the phase constant of which. overv the frequency range to be covered, is proportional to frequency. All of the subsidiary networks have phase constants which are integrally related to each other. To provide a characteristie which, when referred to a constant loss, ls a cosine curve, the required ratios ot these phase constants are 1:3:5: :(Zn-l). Additional units are similarly designed to provide second,

third and higher harmonic curves. The number of units required depends upon the accuracy with which the 'desired insertion loss characteristic is to be simulated. The various units are connected in tandem and coupled in such a way as to reduce interaction between them. Resistance pads may, for example, be used for coupling. Alternatively,

:the units may be located at different points pensating attenuation distortion in long telephone circuits caused, for example, by changes1 in temperature. The number of such units to be used will, of course, depend upon the closeness of regulation required. The phase constants of the auxiliary networks may, in this case, have the ratios 1:2:3:' :12. In order to make the regulation automatic the variable resistors may be of the type having non-linear resistancetemperature characteristics. each under the control of a pilot current of suitable frequency, the amplitude of which reflects the variation of the line attenuation. Perfect compensation is attained at each pilot frequency, and if suicient units are employed and the pilot frequencies are properly distributed any desired limits of regulation throughout the band may be achieved.

The nature of the invention will be more fully understoodA from the following detailed description and by reference to the accompanying drawings in which like reference characters refer to similar or corresponding parts and in which:

Fig. 1 is a schematic circuit, partly in block diagraxmof one form of a variable attenuation unit, in accordance with the invention, comprising n component equalizer sections and having an insertion loss -characteristic corresponding to one term of a Fourier series;

Fig. 2- shows another form of attenuation unit,

to provide a variable attenuation network the over-all insertion loss characteristic of which corresponds to three terms of a Fourier series:

Fig. 5 shows curves which give an indication of how much the insertion loss characteristic of the network of Fig. 1 or Fig. 2, referred to a constant loss, departs from a pure cosine curve when only one or two component equalizer sections are used;

Fig. 6 shows four units of the type shown in Fig. 1, each comprising a single section, which will provide an insertion loss characteristic corresponding to four terms of a Fourier series;

Fig. 7 shows a variable attenuation network similar to the one of Fig. 6 except that each of the umts comprises a single section of the type shown in Fig. 2; and

Fig. 8 is a schematic circuit, partly in block diagram, of an automatic regulating network employing a variable attenuation network of the type shown in Fig. 6 or Fig. 7 andy having four controls actuated by individual pilot currents.

Taking up the figures in more detail, Fig. 1 shows one form of the variable attenuation unit in accordance with the invention which may be so designed that its insertion loss characteristic, when referred to a constant loss, corresponds to one term of a Fourier series. This term may be the fundamental or any of the higher harmonics. The unit has a pair of input terminals i, 2 to which are connected a wave source of impedance Zs and voltage E and a pair of output terminals 9, 'I0 to which the load impedance Zr. is connected. Between the input and output terminals are shown n variable attenuation equalizer sections N1, N2, Ns and.N11, connected in tandem and coupled together in a manner to reduce interaction between the sections. As shown, the coupling means may be the T-type resistance pads P1, P: and Pa. Other means of coupling the sections may, however, be employed. Each of the equalizer sections N1 to N11 is of the type shown in Fig. 11 of the above-mentioned Bode patent. The section N1, for example, comprises a variable impedance branch connected in series between the input impedance Zs and an output impedance Za, which is the impedance looking into the pad Pi at the terminals 3, 4. This series impedance branch comprises a xed resistor Ru to the terminals of whichv are connected the terminals 5, 6 of a four-terminal subsidiary .network M1 which has a constant resistance image impedance and is terminated at its other terminals l, 8 in a variable resistor R21 of value R. The equalizer sections N1, Na and N11 have similarly arranged xed series resistors R12, R1: and R111, respectively, and subsidiary networks Mz, M: and M11 which are terminated, respectively, in the variable resistors R12, Rm and R211.

Equation 23 of the above-mentioned Bode patent shows that, for transmission between terminal impedances Zs and Za, the insertion factor e' for an equalizer section such as N1 may be expressed as 2+ ehi-tank \If 1+'e' tanh Il where :c is the ratio of the terminating resistance R to the image impedance Re of the subsidiary network M1, -lf is the image transfer constant for the network M1, p is a constant and is equal to 0o and e' is the insertion factor for the section when :c is unity. It"\`may be shown from Equation l that Expanding this expression for 0 in a well-known series gives where a is the attenuation constant and is the phase constant or the image transfer constant i' gives 0= (2 UKe-a) en 3e The quantity aUKe-l in parenthesis, which will be denoted by 2, will be independent of frequency if ais independent of frequency. lThe magnitude of C, however, is proportional to U, p which it is seen from Equation 3 can take on all 4 values from -1 to +1. that the veriable terminating resistance R may be varied from zero to infinity. Substituting C for the quantity 2UKe-2 in Equation 9 the series becomes from which it is found that the insertion loss A11 in nepers for the section N1 is A=c' eos 25h22; eos twg; eos 1o+ (11) and the phase shift B1- in radians is If, now, it is assumed that the phase constant is proportional to the frequency f, that is.

=7f (13) e where It is a numerical constant, the insertion 0 less A1 in decibels is given by 05 cos IOkf-l- (14) and the phase shift B4 in degrees is given by. B= 57.3(6' sin w+-16% sin ckf+ gein 10kf+ .A (15) Equation 14 shows that, for the conditions assumed, the insertion loss for a single section auch u as N1 of Fig. 1, referred to a constant loss, is the p anatra sum of a pure cosine curve and the odd har-l monies thereof. The harmonics, however. have considerably less amplitude than the fundamental, and their amplitude decreases rapidly as the orderincreases. In Fig. curve I3 gives the magnitude of the third harmonic in decibels and curve M that of the fifth harmonic, as a function of the magnitude of the fundamental.

In order to obtain a more nearly pure cosine characteristic additional equalizer sections, such as N2, Ne and Nn of Fig. l, may be added in tandem. Eachsection is so designed that its insertion loss, when referred to a constant loss,

is equal in magnitude but opposite in sign to one of the higher order terms of Equation 14. Each added section will, therefore, annui the contri' v That 1S,

In like manner the network N3. is designed to annul the contribution of the third term',

- a=5=5kf (17) The number n of sections to be employed will depend upon the 'allowable deviation from a pure cosine curve for the over-all characteristic. The variable terminating resistors R21. R22. Rza and Ran may be arranged for unitary control, if desired, as indicated by the dashed line l Fig. 3 is a schematic circuit of a network which is suitable for use as the subsidiary fourterminal network M1. It is a constant resistance, all-pass, lattice structure of the type shown, for example, as network 14. in Appendix IV of the paper by O. J. Zobel in the Bell System Technical Journal for July, 1928, pages 438 to 534. It comprises two equal series impedance branches Z1 and two equal lattice impedance branches Z2 which have the relationship Z1Z 2=Ro2 (18) where Rn is the image impedance and is a con'- stant resistance. It may be so designed that its phase constant is substantially proportional to frequency over the range of interest. Since the phase constant z of the network Mz must be equal to 31B, three lattice structures of the type shown in Fig. 3 connected in tandem may be used for this network. Likewise. ve such lattices may be used for the network Ma. and

- (2n-1) for the network Mn.

- Fig. 2 shows another form of they variable attenuation unit, similar to the one of Fig. 1 except that each of the equalizer sections N1, Na, N: and Nn is of the type shown in Figs. 12 and 27 of the above-mentionedBode patent. In this case the variable impedance branch is connected in parallel with the input impedance Zs and the output impedance Za. In the section N1, for example, this shunt branch comprises a fixed resistor R31 having one terminal connected to terminal 5 of the subsidiary fourterminal network M1 which is terminated at its other end in the variable resistor R21. In a similar manner in the other sections the fixed resistors Raz, Rss and Ran are associated. 1

respectively, with the auxiliary networks Mz, Ms and Mn. The tandem connected sections are coupled by means of the resistance pads P1, vPz and Pa. as in Fig. 1. By following the design procedure outlined above the unit shown in Fig. 2 may be designed to provide the same type of over-al1 loss characteristic as that obtainable' with the unit of Fig. l. For a cosine curve the auxiliary networks M1, M2, lVh and Mn will have phase constants which are related in the ratios of odd integers.

Fig. 4 is a schematic circuit, partly in block diagram, of three variable units, S1, S2 and Se, each of the type shown in Fig. 1 or Fig. 2, connected in tandem between the input impedance Ze and the load impedance Zr. and coupled in such a way as to reduce interaction between the units. The coupling means may be the resistance pads P11 and` P12, as shown, or, as a1- ready mentioned, the units may -be located at diii'erent points along a transmission line, separated by sections of the line. Each unit comprises two sections, such as N1 and Nn, and therefore has two controls, such as R21 and R22. Each unit may, of course, comprise any umber of sections, with a corresponding number of controls. One of theunits, say S1,is designed to have a loss characteristic which, when referred to a constant loss, is a cosine curve. The unit Sz is designed to furnish the second harmonic curve, and the unit Se the third harmonic curve.

Additional units may, of course, be employed if higher harmonics are required, The desired characteristic is analyzed on the basisl of a Fourier series of cosine terms. By employing a sufficient number of units, each with a suflicient number of controls, and by properly setting the controls the desired characteristic maybe simulated to` any required degree.

Fig. 6 shows a variable attenuation network similar to the one of Fig. 4 except that it is made u p of four umts, Si to S4. and each unit comprises only a single equalizer section, of the type of N1 of Fig. l, employing-a fixed resistor R11 in a series branch. The section Si is designed to supply the fundamental cosine curve and the sections S2, Ss and Si, respectively, vthe second. third and fourth harmonics. The phase constants of the auxiliary networks M1, M12, M1: and M14 will, therefore, have the ratios 1:2:3:4.

Each of the variable resistors R21, R42, R43 and' of the third harmonic. Therefore-the unit Si,`

which supplies the third harmonic term, may be adjusted to correct for the first neglected term in the fundamental furnished by the unit S1.

Fig. 7 shows a variable network similar to the one of Fig. 6 except that the sections are of the type of Ni of Fig. 2. in which the xed reslstor Rn is in a shunt branch.

Fig. 8 shows a regulating system for automatically equalizing the attenuation distortion caused. lor example, by temperature changes in a long telephone circuit. The distorted signal is impressed upon the input terminals l, 2 of the regulating network Il, which provides the equalization, amplified in the ampliiier I1 and delivered to the load Zr.. The network I6 is of the type shown in Fig. 6 or Fig. 7 but the variable resistors Rn, R42, Ria and R44, which individually control the fundamental and higher order terms, are replaced, respectively, by the thermistors Ti, Ta, Ts and T4, associated, respectively, with the heaters H1, Hz, Ha and H4. These heaters are under the control of individual pilot currents which are taken ofi at the points i8, I9 on the output side oi the amplifier I1 and separated by means of the band-pass filters F1, Fa, Fa and F4. The pilot frequencies are spaced throughout the range to be equalized and each pilot is preferably located in a region where the component characteristic controlled by it makes its maximum contribution to the over-all loss characteristic.

As already pointed out in connection with Fig. 4, the different units or the regulating network may be located at different points along the transmission line, say one at each repeater point.

One unit may, for example, be designed to compensate ior the slope distortion and placed at one repeater point, a second unit, at a second repeater point, may be designed to correct the .so-called bulge distortion, and other units, at

other repeater points, may be designed to compensate for higher order distortion effects. Any required number of units, either greater or less than four, may, of course, be employed.

What is claimed ist 1. In combination, a plurality of tandem connected variable attenuation equalizer sections each comprising terminal impedances and an interposed variable impedance, each of said interposed impedances comprising a fixed resistor in combination with a subsidiary four-terminal network terminated by a variable resistor oi' value R, said subsidiary network having an image impedance Re which is a constant resistance and an image transfer constant if the attenuation constant of which is independent of frequencyv and the phase constant of which is proportional to frequency, in each of said equalizer sections the component impedances being so proportioned with respect to each other that the insertion iactor e0 for transmission between said terminal impedances may be expressedi by the equation ego--tanh If IN1-teoremi 1f e e egli-l-tanh Iv in which said phase constants are related to each other in the ratios of 1:2:3: an integer.

4. The combination in accordance with claim l in which saidphase constants are related to each other in the ratios of 1:3:5:v :(2n-1) where n is an integer.

5. The combination in accordance with claim l in which said interposed variable impedance is connected in series with said terminal impedances.

6. The combination in accordance with claim 1 in which said interposed variable impedance is connected in parallel with said terminal impedances.

7. The combination in accordance with claim 1 in vwhich said fixed resistor is connected in series with said terminal impedances and a pair of terminals of saidl auxiliary network are connected. respectively, to the terminals of said ilxed resistor.

8. The combination in accordance with claim 1 in which one terminal of said xed resistor is connected'to one terminal of each of said terminal impedances, the other terminal of said xed resistor is` connected to one terminal of a pair of terminals of said auxiliary network and the other terminal of said Dairis connected to each of the other terminals of said terminal impedances.

9. The combination in accordance with claim l in which all oi.' said variable resistors are under unitary control.

10. The combination in accordance with claim 1 in which said sections are coupled together by means which reduce the interaction between said sections.

11. The combination in accordance with claim l in which said sections are coupled together by resistance pads.

12. The combination in accordance with claim l in which said variable resistors are thermistors.

13. 'Ihe combination in accordance with claim :n.wherenis 1 in which said sections are coupled together by means which reduce the interaction between said sections and in which all of said variable resistors are under unitary control.

. PAUL H. RICHARDSON. 

